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Rudin Theorem 1.20 (b)

  1. Jul 15, 2012 #1
    I understand the proof except for the following:

    Suppose that -m2 < nx < m1 for positive integers m1, m2, n, and real number x.

    Then there is an integer m with -m2 ≤ m ≤ m1 such that m-1 ≤ nx < m.

    It definitely sounds reasonable, but it seems like a big jump in logic.
  2. jcsd
  3. Jul 15, 2012 #2


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    Gold Member

    Let m be the least integer that is strictly greater than nx. It is a triviality to verify that this integer has the desired properties.
  4. Mar 23, 2013 #3
    Simple proof

    Hi there,
    I have attached a simple demonstration of the bit you are asking.
    Let me know if it is clear now.
    I hope it helps

    Attached Files:

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